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%I #6 Feb 06 2017 03:38:14
%S 0,0,0,1,3,6,10,15,18,22,27,33,37,45,48,52,54,60,60,69,69,79,81,87,79,
%T 93,87,97,99,114,99,120,111,130,126,150,135,168,141,160,147,177,144,
%U 189,156,183,162,201,157,213,171,214,189,231,168,237,189,244,201,261,177,270,201,261,210,282,192,297,216,283,228
%N Expansion of (x + Sum_{p prime, k>=1} x^(p^k))^3.
%C Number of ways to write n as an ordered sum of three prime powers (1 included).
%H Ilya Gutkovskiy, <a href="/A282064/a282064.pdf">Extended graphical example</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimePower.html">Prime Power</a>
%F G.f.: (x + Sum_{p prime, k>=1} x^(p^k))^3.
%e a(6) = 10 because we have [4, 1, 1], [3, 2, 1], [3, 1, 2], [2, 3, 1], [2, 2, 2], [2, 1, 3], [1, 4, 1], [1, 3, 2], [1, 2, 3] and [1, 1, 4].
%t nmax = 70; CoefficientList[Series[(x + Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}])^3, {x, 0, nmax}], x]
%Y Cf. A000961, A098238, A280243, A282062.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, Feb 05 2017